Abelian variety isogeny class 2.37.aq_ev over $\F_{37}$

• Label: 2.37.aq_ev
• Base field: $\F_{37}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{37}$
Dimension:	$2$
L-polynomial:	$1 - 16 x + 125 x^{2} - 592 x^{3} + 1369 x^{4}$
Frobenius angles:	$\pm0.0969535350601$, $\pm0.382359838743$
Angle rank:	$2$ (numerical)
Number field:	4.0.289497.1
Galois group:	$D_{4}$
Jacobians:	$12$
Isomorphism classes:	12

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:	$2$
Slopes:	$[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$887$	$1865361$	$2572200656$	$3510238195161$	$4807418435870327$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$22$	$1364$	$50782$	$1872964$	$69327142$	$2565691094$	$94932529630$	$3512485993348$	$129961764977926$	$4808584392540404$

Jacobians and polarizations

This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=28x^6+30x^5+15x^4+10x^3+19x^2+17x+15$
• $y^2=2x^6+23x^5+30x^4+9x^3+32x^2+19x+23$
• $y^2=8x^6+23x^5+3x^4+22x^3+30x^2+21x+20$
• $y^2=20x^6+22x^5+4x^4+4x^3+26x^2+9x+35$
• $y^2=26x^6+30x^5+26x^4+29x^3+20x^2+31x+5$
• $y^2=17x^6+21x^5+31x^4+14x^3+13x^2+27x+2$
• $y^2=23x^6+26x^5+x^4+21x^3+6x^2+19x+8$
• $y^2=14x^6+25x^5+28x^4+30x^3+26x^2+34x+9$
• $y^2=20x^6+16x^5+4x^4+15x^3+25x^2+12x+32$
• $y^2=12x^6+25x^5+4x^4+20x^3+6x^2+15$
• $y^2=11x^6+21x^5+34x^4+9x^3+12x^2+27x+2$
• $y^2=8x^6+32x^5+30x^4+35x^3+19x^2+22x+24$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{37}$.

Endomorphism algebra over $\F_{37}$

The endomorphism algebra of this simple isogeny class is 4.0.289497.1.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

Twist	Extension degree	Common base change
2.37.q_ev	$2$	(not in LMFDB)